The general Characteristics of the frequencyfunction of stellar movements 



27 



(55) 



V# 2 



V#n 



02 



11 



(1 

 (1 

 (1 



2')^/o 2 



V #,0 = v 30 g' 3 - 3v 20 * 0 (1 - g' 2 ) g' + * 0 3 (2 - 2g' + g' 3 ) 



'V K n = v 2i ?' 3 - bo v 20 + 2* 0 v u ) (1 - g' + r 0 2 y 0 (2 - 3g' + g' 3 ) 

 ( 5J> ) V = v M g' 3 - K v 02 + 2y 0 v u ) (1 - g' 2 ) g' + x 0 y 0 > (2 - 3g' + g' 3 ) 



V #03 = \ s 2' 3 - 3v 02 y 0 (1 - g' 2 ) g' + */ 0 3 (2 - 3g' + g' 3 ) 



(55**) 



M#4o - 3#o 3 ) = v 40 2' 6 -4v 30 ^o(l-?' 3 ) g' 3 +6v 20 V(2-g'-2g' 2 + g' 5 ) g'- 



- 3v 20 2 g' 2 - V(6 - 12g' + 3g' 2 + 4g' 3 - g' 6 ) 

 V(JV,i - 3#,o #n) = V B1 g" ! - (3v 21 X 0 + v 30 y 0 ) (1 - g' 3 ) g' 3 + 



+ 3 (v u » 0 f + v io - r o y 0 ) (2-g— 2g' 2 + g' 5 ) g' — 3v 20 v u g' 2 — 

 -12g'+3g' 2 + 4g' 3 -g' 6 ) 

 V(# 22 -# 2 o#o2-2#n 2 ) = ^2' 6 - 2(v 12 .r 0 + v 21 //o ) (1 - g' 3 ) g' 3 + 



+ (4v u * 0 ?/„ + v 20 */ 0 2 + v 02 x 0 2 ) (2 - g' - 2g' 2 + g' 5 ) g' - 



- (2v u 2 + v 20 v 02 ) g' 2 - * 0 2 y 0 '(6 - 1 2g' + 3g' 2 + 4g' 3 - g' 6 ) 

 V(#is - 3iV 02 N n ) = v 13 g' 6 - (3v 12 y 0 + v 03 x 0 ) (1 - g' 3 ) g' 3 4- 



+ 3(v n y* + v 03 .r o//o ) (2 -g' - 2g' 2 + g 5 ) g'-3v 02 v u g' 2 - 

 -*o - 12g' + 3g' 2 4- 4g' 3 - g' 6 ) 

 V(#„4 - 3iV 02 2 ) = v 04 g' 6 -4 v 03 y 0 (l -g' 3 ) g' 3 4- 6v 02 y/ 0 2 (2 -g' -2g' 2 +g' 5 ) g'- 



- 3v û2 g' 2 - y 0 *(6 - 12g' + 3g' 2 + 4g' 3 - g' 6 ). 



By those equations the moments of the linear motions for the stars within a 

 small area of the sky, are expressed through the moments of the apparent motion. 



